Although educated as a mechanical engineer, electronics have always stumped me. Here's my problem...

Per request from my Mrs., I constructed a 'little library' for the front of my home and would like to put solar/rechargeable battery powered LED lights in it. I purchased an Alpine Corp SLA200SB garden light. It came with (2) white light LEDs (connected in parallel) powered by one 1.2 V, 600mAh, size AA battery, a small circuit board (containing a 40 Ohm resistor), an 'ON/OFF' switch, and a solar charger. I disassembled it, tagging each lead to show where it went. I bought new battery holder for (2) size AA batteries, and modified it so the batteries would be in parallel rather than in series. The new size AA batteries are from Radio Shack, re-chargeable Enercells, each 1.2 V, 2500 mAh. I then reassembled everything, adding add'l length leads as I thought appropriate for my project. All splices were soldered and insulated. I left the new assembly under a 60 watt bulb overnight to charge the batteries, making sure the switch was 'OFF'. The batteries charged for approx. 10 hrs. In the morning, I checked to ensure the batteries were charged. My volt meter indicated 1.2 V's. I covered the solar panel and turned the switch to 'ON', expecting the LEDs to light up. They didn't. Using my volt meter, I checked to ensure the LEDs were getting power. The meter indicated 1.2 V's. What did I do wrong? What should I do to get the LEDs to light?